A parallel plate capacitor with air as the dielectric has capacitance C.A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure.The new capacitance will be

Options

A. `(k+3) C/4`
B. `(k+2) C/4`
C. `(k+1) C/4`
D. `(kC)/4`

Answer

A

Explanation

`C_(eq) =C_1+C_2=((A/4)epsilon_0k)/d+(((3A)/(4))epsilon_0)/d`
`=(Aepsilon_0)/d [k/4+3/4] =C/4 (k+3)`